1/1×4＋1/4×7＋1/7×14＋…＋1/97×100 简便计算过程,/是分数线,÷是除号
问题描述：
1/1×4＋1/4×7＋1/7×14＋…＋1/97×100 简便计算过程,/是分数线,÷是除号
答
1/(1*4)+1/(4*7)+1/(7*10)+.+1/(97*100)
=1/3*(1-1/4)+1/3*(1/4-1/7)+1/3*(1/7-1/10)+.+1/3*(1/97-1/100)
=1/3*(1-1/4+1/4-1/7+1/7-1/10+.+1/97-1/100)
=1/3*(1-1/100)
=33/100